1. Introduction

Bacteria are the dominant form of life spread across the whole planet. Their biochemistry machinery is well adapted to scarcity conditions; also, they can biosynthesize complex molecules in various environmental conditions. For this reason, the growth and proliferation of bacteria in controlled environments represent an interest of biochemical engineers, microbiologists, and cell-growth enthusiasts since they allow bioprocess simulation and control scheme design. Substrate transformations into cell biomass, organic molecules, therapeutic proteins, biofuels, enzymes, and food additives are of attention since application to actual fields and laboratory experiments are very difficult to scale-up to industrial level with strict and complete control of key variables determined as an ideal process [1]. It is known that the complexity in a mathematical model may increase with the inclusion of environmental conditions such as multisubstrate consumption and product formation, pH change during fermentation, variable temperature, rheological changes in culture media, multiphasic environmental variability, and nonideality of mixing and stirring [2]. The kinetic model had been evolved from simple exponential growth to complex mathematical expressions to predict heterogeneity in single cells, describe multiple reactions, explain internal control mechanisms, and even predict genetic variability between bacterial populations [3]. However, despite the efforts to represent the progress of biological reactions in microbial cultures, the actual application of the model in real production processes is impractical due to a significant amount of information fed to the model [4].

Many of the kinetic growth models base their structure on and take information from empirical observations through experimental data. The white box models (WBMs) use information from mass balances in a single stoichiometric equation where inputs, outputs, and the conversion from substrates to products are followed [5]. Despite effectiveness and advanced reaction representation in WBMs, the representation of the reaction advance degree, some information on metabolic flux analysis (MFA) can be obtained. Models based on detailed MFA can be used to define optimal operation conditions based on biochemical pathways. It has been established that kinetic models of biological reactions are more complicated than "common" chemical reaction models. Microbial growth models require specialized knowledge of rapid changes of environmental conditions, stoichiometric individual reactions, and the appearance of new steady states in different culture stages [6]. In many cases, mechanistic models, based on first principles, are ineffective because of metabolic complexity of microorganisms.

solid or semisolid, and gaseous phases (e.g. solid-state fermentation). Within this

In this chapter, we provide an overview of mechanistic and empirical models for

Unstructured kinetic models (UKMs) represent, in a simple global point of view,

To get the most efficient description of a kinetic model, it is essential to be clear about the application purpose. The application determines the complexity level and structure of the model. The correlation among cell growth, substrate consumption and inhibition [7], or description of the substrate profiles within the reactor during expression of extracellular proteins is the central goal of the model process [8]. The description of key variables is the contribution of the model [9]. These representations are expressed as equations in a simple mathematical model. The UKMs, which are unstructured, unsegregated, are based on the monitoring of cell and nutrient concentration and describe the fermentation process as an average of the species under ideal conditions. Also, it describes the cell and its components as a single species in solution. UKMs consider the apparent rate obtained by metabolic processes, which are carried out by microorganisms. These models are based on conservation equations for cell mass, nutrients, metabolites, and species generation/ consumption rates. Most of the UKMs can be divided into three terms: rate expressions for cell growth, rate expressions for nutrient uptake, and rate expressions for

In the case of exponential growth phase, which is the simplest representation of microbial growth, nutrient concentration profiles and decrease rate in several cases

> ri <sup>¼</sup> <sup>α</sup> Yi dX

where r is the reaction rate, X represents biomass, μ is specific growth rate, kD is

The simplest example of multiple reaction models includes substrate consumption for cell maintenance and true yield coefficients (g DCW/g DW) [5]. One of the

dt <sup>¼</sup> ð Þ� <sup>μ</sup> � kD <sup>X</sup> (1)

dt (2)

rX <sup>¼</sup> dX

the death rate, α is the stoichiometric factor, and Yi is the yield.

the metabolic behavior of the biomass cell production. Mainly, mathematical descriptions for microbial growth kinetics in fermentation processes are based on semiempirical observations. From simple experimental data, we can obtain infor-

mation to represent cellular growth with unstructured kinetic models.

classification, parameters in a model can be classified as distributed and nondistributed (lumped). Distributed parameter models assume that operation parameters vary as a function of space. One, two, or three dimensions are considered in the description of key variables as a function of parameter distribution. As a result, the system is described by a set of partial differential equations (PDEs). On the other hand, a lumped model is necessary, and the system can be described by a set of ordinary differential equations (ODEs), since these parameters do not vary as

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

DOI: http://dx.doi.org/10.5772/intechopen.82195

a function of space.

metabolite production.

13

are not almost considered.

cell population in fermentation processes.

2. Simple and unstructured kinetic growth models

2.1 Unstructured kinetic models for simple systems

In this sense, complex microbial consortium behavior and culture media with different types of substrates are difficult to model. Nonmechanistic models, or black box models (BBMs), or a combination between mechanistic and nonmechanistic models, or gray box models (GBMs), are more suitable to describe them. Kinetic parameter fitting for WBMs requires experimental measurements of multiple variables, and frequently, model validation may be impractical. BBMs and GBMs constitute alternatives which describe the general dynamic behavior of bioreactors, without requiring many experimental measurements of the system. These models do not offer mechanistic information about metabolic phenomenology present in the system, but they can optimize and control without it. Then, models can be classified based on the mathematical formulation of the system (Figure 1). These are classified into mechanistic, empirical, and fermentation models. A mechanistic model is based on deterministic principles. On the other hand, empirical models represent input-output relations without the knowledge of a mechanism. Fermentation process models are usually represented with a combination of both, mechanistic and empirical models.

An important characteristic of modeling is the assumption of homogeneous or heterogeneous conditions. In this sense, a homogeneous system is related to a single continuous phase. In most cases, bioreactors are described as single liquid phases. However, if the biofilm is included in the study, a solid or semisolid phase needs to be considered in the model. On the other hand, heterogeneous systems are related to the description of two or more continuous phases and the interactions between them. Complex heterogeneous systems can be described as multiple phases: liquid,

Figure 1. Classification of models as mechanistic and nonmechanistic.

Fermentation: Metabolism, Kinetic Models, and Bioprocessing DOI: http://dx.doi.org/10.5772/intechopen.82195

Many of the kinetic growth models base their structure on and take information

In this sense, complex microbial consortium behavior and culture media with different types of substrates are difficult to model. Nonmechanistic models, or black box models (BBMs), or a combination between mechanistic and nonmechanistic models, or gray box models (GBMs), are more suitable to describe them. Kinetic parameter fitting for WBMs requires experimental measurements of multiple variables, and frequently, model validation may be impractical. BBMs and GBMs constitute alternatives which describe the general dynamic behavior of bioreactors, without requiring many experimental measurements of the system. These models do not offer mechanistic information about metabolic phenomenology present in the system, but they can optimize and control without it. Then, models can be classified based on the mathematical formulation of the system (Figure 1). These are classified into mechanistic, empirical, and fermentation models. A mechanistic model is based on deterministic principles. On the other hand, empirical models represent input-output relations without the knowledge of a mechanism. Fermentation process models are usually represented with a combination of both, mecha-

An important characteristic of modeling is the assumption of homogeneous or heterogeneous conditions. In this sense, a homogeneous system is related to a single continuous phase. In most cases, bioreactors are described as single liquid phases. However, if the biofilm is included in the study, a solid or semisolid phase needs to be considered in the model. On the other hand, heterogeneous systems are related to the description of two or more continuous phases and the interactions between them. Complex heterogeneous systems can be described as multiple phases: liquid,

from empirical observations through experimental data. The white box models (WBMs) use information from mass balances in a single stoichiometric equation where inputs, outputs, and the conversion from substrates to products are followed [5]. Despite effectiveness and advanced reaction representation in WBMs, the representation of the reaction advance degree, some information on metabolic flux analysis (MFA) can be obtained. Models based on detailed MFA can be used to define optimal operation conditions based on biochemical pathways. It has been established that kinetic models of biological reactions are more complicated than "common" chemical reaction models. Microbial growth models require specialized knowledge of rapid changes of environmental conditions, stoichiometric individual reactions, and the appearance of new steady states in different culture stages [6]. In many cases, mechanistic models, based on first principles, are ineffective because of

metabolic complexity of microorganisms.

Current Topics in Biochemical Engineering

nistic and empirical models.

Figure 1.

12

Classification of models as mechanistic and nonmechanistic.

solid or semisolid, and gaseous phases (e.g. solid-state fermentation). Within this classification, parameters in a model can be classified as distributed and nondistributed (lumped). Distributed parameter models assume that operation parameters vary as a function of space. One, two, or three dimensions are considered in the description of key variables as a function of parameter distribution. As a result, the system is described by a set of partial differential equations (PDEs). On the other hand, a lumped model is necessary, and the system can be described by a set of ordinary differential equations (ODEs), since these parameters do not vary as a function of space.

In this chapter, we provide an overview of mechanistic and empirical models for cell population in fermentation processes.

## 2. Simple and unstructured kinetic growth models

Unstructured kinetic models (UKMs) represent, in a simple global point of view, the metabolic behavior of the biomass cell production. Mainly, mathematical descriptions for microbial growth kinetics in fermentation processes are based on semiempirical observations. From simple experimental data, we can obtain information to represent cellular growth with unstructured kinetic models.

#### 2.1 Unstructured kinetic models for simple systems

To get the most efficient description of a kinetic model, it is essential to be clear about the application purpose. The application determines the complexity level and structure of the model. The correlation among cell growth, substrate consumption and inhibition [7], or description of the substrate profiles within the reactor during expression of extracellular proteins is the central goal of the model process [8]. The description of key variables is the contribution of the model [9]. These representations are expressed as equations in a simple mathematical model. The UKMs, which are unstructured, unsegregated, are based on the monitoring of cell and nutrient concentration and describe the fermentation process as an average of the species under ideal conditions. Also, it describes the cell and its components as a single species in solution. UKMs consider the apparent rate obtained by metabolic processes, which are carried out by microorganisms. These models are based on conservation equations for cell mass, nutrients, metabolites, and species generation/ consumption rates. Most of the UKMs can be divided into three terms: rate expressions for cell growth, rate expressions for nutrient uptake, and rate expressions for metabolite production.

In the case of exponential growth phase, which is the simplest representation of microbial growth, nutrient concentration profiles and decrease rate in several cases are not almost considered.

$$r\_X = \frac{dX}{dt} = (\mu - k\_D) \cdot X \tag{1}$$

$$r\_i = \frac{a}{Y\_i} \frac{dX}{dt} \tag{2}$$

where r is the reaction rate, X represents biomass, μ is specific growth rate, kD is the death rate, α is the stoichiometric factor, and Yi is the yield.

The simplest example of multiple reaction models includes substrate consumption for cell maintenance and true yield coefficients (g DCW/g DW) [5]. One of the most used UKMs is Monod's model [10]. This is one of the simplest models to deal with microbial growth, physiology, and biochemistry. The Monod equation describes the proportional relationship between the specific growth rate and low substrate concentrations (Eq. (3)).

$$
\mu = \frac{\mu\_{\text{MAX}}[\text{S}]}{K\_{\text{S}} + [\text{S}]} \tag{3}
$$

growth, fermentations present catabolic inhibition. Therefore, several research groups propose complete UKMs, which include the empirical observation such as variables regarding cells, substrates, and products. Hans and Levenspiel [15] proposed a kinetic model that assumes the existence of inhibitor critical

� � !ni " # ½ � <sup>S</sup>

The inhibition function proposed by Levenspiel [16] takes into account the inhibition of ethanol production of alcoholic fermentation modeling, where subscript i corresponds to the substrate or product concentrations. Linear (n, m ¼ 1), nonlinear (n, m > 1), and fractional (n, m ¼ 0:5) applications of these models are possible for fermentation bioreactors (Eq. (7)). An extension of the model was proposed by Luong [7]. He assumes a common mechanism to describe substrate inhibition. Inhibitory factors acting simultaneously could be represented by the

> ½ � S ½ �þ S KS

where [P] is the product species concentration and n is the index of

� � <sup>1</sup> � ½ � <sup>P</sup>

These models can also explain multiple reactions and include biochemical information of metabolites in the global net effect, making them experimentally accurate. This characteristic is useful for structured and segregated modeling [17]. These models can also describe mixed metabolism [18] and hetero-fermentations [19]. The duality of Saccharomyces cerevisiae metabolism, aerobic and anaerobic metabolism, is the best example of multiple reactions. The aerobic growth of the yeast yields biomass by favoring metabolic pathways designed for anabolism and cell division. This metabolism is oxidative in amphibolic reactions. However, at low oxygen concentrations, the yeast metabolism changes from being purely respiratory to partially fermentative. The fermentative pathway mainly leads to ethanol production as a final electron acceptor. Thus, there is a limited growth with high ethanol yields in fermentation culture media. Both metabolisms can occur during the growth of S. cerevisiae in a wide range of simple carbohydrate fermentations. At high substrate concentrations, there are limitations in respiratory pathways, which lead to an overflow to ethanol production with enhanced fermentative pathways. The simple WBM with overall reactions could not explain in detail the dualism of both fermentative and respiratory metabolisms. Thus, there are two stoichiometric reactions proposed to explain oxidative and fermentative metabolisms [18].

½ � PMAX � �<sup>n</sup>

γ1X þ β11CO<sup>2</sup> � S � α12O<sup>2</sup> ¼ 0 (9)

γ2X þ β21CO<sup>2</sup> þ β22P � S ¼ 0 (10)

This system considers nearly ideal Monod kinetics, no by-product formation, linear specific oxygen consumption rate, and correlation with substrate uptake. If the primary carbon source is glucose (instead of ethanol), glucose can be used

0

BBB@

½ �þ S KS

Q h i¼1

<sup>1</sup> � Ii ½ � I ∗ <sup>i</sup> ½ � � �mi � �

1

CCCA

(7)

(8)

concentrations.

following equation:

15

cooperativity between inhibitors.

<sup>μ</sup> <sup>¼</sup> <sup>μ</sup>MAX <sup>Y</sup>

DOI: http://dx.doi.org/10.5772/intechopen.82195

h

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

<sup>1</sup> � Ii ½ � I ∗ i

i¼1

where [I] is the inhibitor species concentration.

μ ¼ μMAX

where α, β, and γ are stoichiometric coefficients.

where μMAX is the maximum specific growth rate, [S] is the substrate concentration, and KS is the saturation constant.

The disadvantage of the model is that the individual entity, regulatory complex, adaptive response to environmental changes, and capacity of cell organelles to generate various products in inherent metabolism cannot be considered. The simplest mathematical models used to estimate microbial growth and substrate consumption are still used for monoclonal antibody production by Chinese hamster ovary (CHO) cells [11, 12]. UKMs can predict specific growth rate in simple systems by calculation of mass balances with independent variables.

#### 2.2 Unstructured kinetic models for a more complicated system

The Monod equation is not able to predict the substrate inhibition effect. Thus, several models including such effects have been developed. For example, Andrew's kinetic equation includes an inhibition function to relate substrate concentration and specific growth rate [13].

$$\mu = \frac{\mu\_{\text{MAX}}}{1 + K\_{\text{S}}/[\text{S}] + [\text{S}]/K\_{\text{i}}} \tag{4}$$

where Ki is the substrate inhibition parameter.

Under the assumption of steady state in continuous operation, substrate concentration is low, and the term ½ � S =Ki is neglected. Under these conditions, specific growth rate of Andrew's kinetic equation follows Monod equation [13]. Another inhibition function is Aiba's equation for alcoholic fermentation.

$$\mu = \frac{\mu\_{MAX}[\mathbf{S}]}{K\_{\mathcal{S}} + [\mathbf{S}]} e^{(-[P]/K\_i)} \tag{5}$$

where [P] is the product concentration.

Under the assumption of low product concentration, the term ½ � P =Ki ≈ 0, resulting in a simplification to Monod equation [13].

The Monod model assumes that the fermentation culture media has only one limiting substrate. More than one limiting substrate is present and impacts specific growth rate. Thus, the following model considering multiple substrates is proposed [14].

$$\mu = \left( \mathbf{1} + \sum\_{i}^{n} \frac{[\mathbf{S}\_{\epsilon,i}]}{[\mathbf{S}\_{\epsilon,i}] + K\_{\epsilon,i}} \right) \left[ \prod\_{j}^{n} \frac{\mu\_{\text{MAX},j} [\mathbf{S}\_{j}]}{[\mathbf{S}\_{j}] + K\_{\mathbf{S},j}} \right] \tag{6}$$

where subscript i is the number of each substrate species and e represents the essential substrate.

The limited but accurate information provided by UKMs may help to represent global reactions effectively. In addition to substrate consumption and microbial

Fermentation: Metabolism, Kinetic Models, and Bioprocessing DOI: http://dx.doi.org/10.5772/intechopen.82195

most used UKMs is Monod's model [10]. This is one of the simplest models to deal with microbial growth, physiology, and biochemistry. The Monod equation describes the proportional relationship between the specific growth rate and low

<sup>μ</sup> <sup>¼</sup> <sup>μ</sup>MAX½ � <sup>S</sup>

where μMAX is the maximum specific growth rate, [S] is the substrate concen-

The disadvantage of the model is that the individual entity, regulatory complex,

The Monod equation is not able to predict the substrate inhibition effect. Thus, several models including such effects have been developed. For example, Andrew's kinetic equation includes an inhibition function to relate substrate concentration

1 þ KS=½ �þ S ½ � S =Ki

Under the assumption of steady state in continuous operation, substrate concentration is low, and the term ½ � S =Ki is neglected. Under these conditions, specific growth rate of Andrew's kinetic equation follows Monod equation [13]. Another

<sup>μ</sup> <sup>¼</sup> <sup>μ</sup>MAX

<sup>μ</sup> <sup>¼</sup> <sup>μ</sup>MAX½ � <sup>S</sup> KS <sup>þ</sup> ½ � <sup>S</sup> <sup>e</sup>

limiting substrate. More than one limiting substrate is present and impacts specific growth rate. Thus, the following model considering multiple substrates is

> Se,i ½ � Se,i ½ �þ Ke,i � � <sup>Y</sup><sup>n</sup>

where subscript i is the number of each substrate species and e represents the

The limited but accurate information provided by UKMs may help to represent global reactions effectively. In addition to substrate consumption and microbial

j

μMAX,j Sj � �

" #

Sj � � <sup>þ</sup> KS,j

Under the assumption of low product concentration, the term ½ � P =Ki ≈ 0,

The Monod model assumes that the fermentation culture media has only one

adaptive response to environmental changes, and capacity of cell organelles to generate various products in inherent metabolism cannot be considered. The simplest mathematical models used to estimate microbial growth and substrate consumption are still used for monoclonal antibody production by Chinese hamster ovary (CHO) cells [11, 12]. UKMs can predict specific growth rate in simple systems

by calculation of mass balances with independent variables.

where Ki is the substrate inhibition parameter.

where [P] is the product concentration.

resulting in a simplification to Monod equation [13].

μ ¼ 1 þ ∑

n i

inhibition function is Aiba's equation for alcoholic fermentation.

2.2 Unstructured kinetic models for a more complicated system

KS <sup>þ</sup> ½ � <sup>S</sup> (3)

ð Þ �½ � <sup>P</sup> <sup>=</sup>Ki (5)

(4)

(6)

substrate concentrations (Eq. (3)).

Current Topics in Biochemical Engineering

tration, and KS is the saturation constant.

and specific growth rate [13].

proposed [14].

essential substrate.

14

growth, fermentations present catabolic inhibition. Therefore, several research groups propose complete UKMs, which include the empirical observation such as variables regarding cells, substrates, and products. Hans and Levenspiel [15] proposed a kinetic model that assumes the existence of inhibitor critical concentrations.

$$\mu = \mu\_{MAX} \left[ \prod\_{i=1}^{h} \left( 1 - \frac{[I\_i]}{[I\_i^\*]} \right)^{n\_i} \right] \left( \frac{[\text{S}]}{[\text{S}] + K\_S \left[ \prod\_{i=1}^{h} \left( 1 - \frac{[I\_i]}{[I\_i^\*]} \right)^{m\_i} \right]} \right) \tag{7}$$

where [I] is the inhibitor species concentration.

The inhibition function proposed by Levenspiel [16] takes into account the inhibition of ethanol production of alcoholic fermentation modeling, where subscript i corresponds to the substrate or product concentrations. Linear (n, m ¼ 1), nonlinear (n, m > 1), and fractional (n, m ¼ 0:5) applications of these models are possible for fermentation bioreactors (Eq. (7)). An extension of the model was proposed by Luong [7]. He assumes a common mechanism to describe substrate inhibition. Inhibitory factors acting simultaneously could be represented by the following equation:

$$\mu = \mu\_{MAX} \left( \frac{[\text{S}]}{[\text{S}] + K\_S} \right) \left( \mathbf{1} - \frac{[P]}{[P\_{MAX}]} \right)^n \tag{8}$$

where [P] is the product species concentration and n is the index of cooperativity between inhibitors.

These models can also explain multiple reactions and include biochemical information of metabolites in the global net effect, making them experimentally accurate. This characteristic is useful for structured and segregated modeling [17]. These models can also describe mixed metabolism [18] and hetero-fermentations [19]. The duality of Saccharomyces cerevisiae metabolism, aerobic and anaerobic metabolism, is the best example of multiple reactions. The aerobic growth of the yeast yields biomass by favoring metabolic pathways designed for anabolism and cell division. This metabolism is oxidative in amphibolic reactions. However, at low oxygen concentrations, the yeast metabolism changes from being purely respiratory to partially fermentative. The fermentative pathway mainly leads to ethanol production as a final electron acceptor. Thus, there is a limited growth with high ethanol yields in fermentation culture media. Both metabolisms can occur during the growth of S. cerevisiae in a wide range of simple carbohydrate fermentations. At high substrate concentrations, there are limitations in respiratory pathways, which lead to an overflow to ethanol production with enhanced fermentative pathways. The simple WBM with overall reactions could not explain in detail the dualism of both fermentative and respiratory metabolisms. Thus, there are two stoichiometric reactions proposed to explain oxidative and fermentative metabolisms [18].

$$
\gamma\_1 \mathbf{X} + \beta\_{11} \mathbf{CO}\_2 - \mathbf{S} - a\_{12} \mathbf{O}\_2 = \mathbf{0} \tag{9}
$$

$$
\rho\_2 \mathbf{X} + \rho\_{21} \mathbf{C} \mathbf{O}\_2 + \rho\_{22} \mathbf{P} - \mathbf{S} = \mathbf{0} \tag{10}
$$

where α, β, and γ are stoichiometric coefficients.

This system considers nearly ideal Monod kinetics, no by-product formation, linear specific oxygen consumption rate, and correlation with substrate uptake. If the primary carbon source is glucose (instead of ethanol), glucose can be used

aerobically and anaerobically. Ethanol can be used as a carbon source only aerobically. Then, different sets of linear algebraic equations can be derived concerning carbon, oxygen, and hydrogen balance.

The respiratory quotient (RQ ) is often used as an indicator of fermentative processes. When RQ is close to one, there is no fermentative metabolism, whereas if RQ is above one, the fermentative metabolism occurs.

$$RQ = \left| \frac{r\_{CO\_2}}{r\_{O\_2}} \right| = \begin{cases} > \mathbf{1}, \text{fermentative metalolism} \\ \approx \mathbf{1}, non \text{fermentative metalolism} \end{cases} \tag{11}$$

presence of metabolite concentration changes, the network structure represents the reaction and metabolite concentration as a matrix array. Then, SKMs can be classified as dynamic and structural [21]. Dynamic models are described as a set of ordinary differential equations (ODEs). Structural models, which are simplified from ODEs, are represented by a set of algebraic equations through two main

The structured and unstructured kinetic models in the previous sections describe, with a high degree of accuracy, the dynamic behavior of microbial growth in bioreactors. These models, associated with material and energy balances, also help to understand the phenomena associated with microbial metabolism, giving

(SMs) and artificial intelligence tools (AITs). SMs use experimental design, response surface analysis, and exploratory data analysis, whereas AITs consider tools such as data mining, artificial networks, and fuzzy logic [22]. Also, several methodologies to combine mechanistic approaches with nonmechanistic modeling strategies have been developed. The hybrid models, which are known as gray box models (GBMs), inherit the advantages of BBMs such as data analysis and can achieve semi-mechanistic description to each metabolic phenomenon. GBMs offer greater estimation accuracy, calibration ease, better extrapolation properties, and more detailed information on the phenomenology of the system [23]. The advantages of GBMs in the application of bioreactor modeling are direct control and optimization. In this section, we will describe some of these nonmechanistic modeling tools and some of their applications, such as the design of soft sensors.

Black box models (BBMs) usually fall into two main categories: statistical models

Artificial neural networks (ANNs) are mathematical models that are devised from the need to characterize biological neural processes. As the system of ANNs imitates the way which is used to interact with each other in brain neuron, ANNs are simple and strong processes to interconnect the elements that transmit and process information through electrical impulses. In ANNs, these simple process elements are also known as neurons, and depending on the complexity of the connection schemes, they can develop the ability to describe the nonlinear behavior of many dynamic systems [24]. ANNs are computational models that aim to achieve mathematical formalizations of the brain structure and functions, which are constantly reformed by learning through experience and extracting knowledge from the same experience. In ANNs, the hierarchical structure similar to that in brain is established, where neurons connect with each other and transmit the response to other neurons. Once the ANN's structure is defined, it is necessary to develop memory form experience (experimental data). In order to introduce this experience, the ANN training algorithm performs a weight (ω) fitting process associated with each neuron, such that the actions introduced (input signals) converge to the reactions produced (output signal) [24]. Although ANNs do not provide a physical interpretation of the phenomena that take place in the system, these models can approximate the dynamic behavior of the system, making them suitable universal approximators [22]. ANNs are defined based on three basic characteristics: their architecture, activation functions, and training algorithm. The architecture deals with the type of interconnections between their processing units or neurons, while

approaches: MFA and elementary mode analysis (EMA).

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

DOI: http://dx.doi.org/10.5772/intechopen.82195

4. Nonmechanistic models

4.1 Neural network models

17

clues to the process design and control.

The mechanistic characteristics of an unstructured, unsegregated kinetic model contribute to the knowledge of the complex metabolism of S. cerevisiae. Despite giving relevant information of simple metabolic processes with multiple reactions, UKMs cannot give information about complete intracellular oxidative metabolism. An example of the application of these models is explained in subsequent sections.
